Answer: x-2y=2
Given the equation of the line below.
[tex]y=\frac{1}{2}x+3[/tex]
We are to determine the equation which represents a line parallel to y.
Two lines are said to be parallel if they have the same slope.
Thus, in order to compare slopes, express each of the given options in the slope-intercept form by making y the subject.
Option 1
[tex]\begin{gathered} y-2x=-5 \\ y=2x-5 \\ \text{Slope}=2 \end{gathered}[/tex]
Option 2
[tex]\begin{gathered} 2x+y=-6 \\ y=-2x-6 \\ \text{Slope}=-2 \end{gathered}[/tex]
Option 3
[tex]\begin{gathered} x-2y=2 \\ 2y=x-2 \\ y=\frac{x}{2}-\frac{2}{2} \\ y=\frac{1}{2}x-1 \\ \text{Slope }=\frac{1}{2} \end{gathered}[/tex]
The equation x-2y=2 has a slope of 1/2.
Therefore, the parallel line is x-2y=2.
